How to Calculate Compound Interest — Formula & Examples
Compound interest is often called the eighth wonder of the world — it's the process of earning interest on your interest. The compound interest formula is A = P(1 + r/n)^(nt). Understanding it is essential for retirement planning, savings accounts, and understanding debt.
The Compound Interest Formula
A = P × (1 + r/n)^(n×t)
A
Final amount (principal + interest)
P
Principal (initial investment)
r
Annual interest rate (as decimal)
n
Compounding frequency per year
t
Time in years
Compound Interest Calculator
Final Amount
$20,097
Interest Earned
$10,097
Growth
101.0%
$10,000 Growth at 7% (Monthly Compounding)
| Years | Total Value | Interest Earned | Growth |
|---|---|---|---|
| 1 year | $10,723 | +$723 | +7% |
| 5 years | $14,176 | +$4,176 | +42% |
| 10 years | $20,097 | +$10,097 | +101% |
| 15 years | $28,489 | +$18,489 | +185% |
| 20 years | $40,387 | +$30,387 | +304% |
| 25 years | $57,254 | +$47,254 | +473% |
| 30 years | $81,165 | +$71,165 | +712% |
Frequently Asked Questions
What is the compound interest formula?
A = P × (1 + r/n)^(nt), where P = principal, r = annual interest rate (decimal), n = compounding frequency per year, t = time in years. The result A is the total amount including interest.
How often should interest compound for maximum growth?
The more frequently interest compounds, the more you earn. Daily compounding earns slightly more than monthly, which earns more than annual. However, the difference between daily and monthly is usually less than 0.1%.
What is the Rule of 72?
The Rule of 72 estimates how long it takes to double your money: Years to double = 72 ÷ Interest Rate. At 8% annual return, your money doubles in approximately 9 years (72 ÷ 8 = 9).
What is the difference between simple and compound interest?
Simple interest is calculated only on the principal. Compound interest is calculated on the principal plus accumulated interest. Over time, compound interest grows exponentially while simple interest grows linearly.
How does compound interest work against you in debt?
Credit card debt compounds monthly at high rates (18–29% APR). A $5,000 balance at 20% APR compounds to $6,107 after one year if unpaid — you owe $1,107 in interest alone.
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Rule of 72
At 7% return, your money doubles every ~10.3 years.
Formula: 72 ÷ 7 = 10.3 years